{
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  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "┌ Info: Precompiling Plots [91a5bcdd-55d7-5caf-9e0b-520d859cae80]\n",
      "└ @ Base loading.jl:1664\n"
     ]
    }
   ],
   "source": [
    "using Plots"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "r (generic function with 1 method)"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "r(i, t) = iseven(i) ? sin(t/M^(2i/p)) : cos(t/M^(2i/p))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "M = 10^4\n",
    "p = 768\n",
    "T = 4000;"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "pos_embeddings = [r(i, t) for t in 1:T, i in 1:p];"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(4000, 768)"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "size(pos_embeddings)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
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   "source": [
    "heatmap(pos_embeddings[1:60,1:200]', yflip = false, \n",
    "        legend = false, \n",
    "        xlabel = \"Time index\", \n",
    "        ylabel = \"Embedding vector index\",\n",
    "        c = :thermal,\n",
    "        guidefontsize = 14)"
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  {
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   "execution_count": 7,
   "metadata": {},
   "outputs": [
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     "data": {
      "text/plain": [
       "\"/Users/uqjnazar/Dropbox/MathEngDeepLearningBook/LaTeXBook/figures/chapter_7_figures/pos_embedding_matrix_plot.pdf\""
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     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "savefig(\"/Users/uqjnazar/Dropbox/MathEngDeepLearningBook/LaTeXBook/figures/chapter_7_figures/pos_embedding_matrix_plot.pdf\")"
   ]
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  {
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       "  1825.8,710.955 1835.39,733.179 1844.98,712.061 1854.56,733.975 1864.15,713.15 1873.73,734.625 1883.32,714.21 1892.91,735.144 1902.49,715.233 1912.08,735.548 \n",
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       "  \n",
       "  \"/>\n",
       "</svg>\n"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "plot(pos_embeddings[50,1:200] - pos_embeddings[51,1:200],\n",
    "        label=false,\n",
    "        xlabel = \"Embedding vector index\",\n",
    "        ylabel =\"Difference between\\n t=50 and t=51\",\n",
    "        ylim=(-1,1),\n",
    "        c=:black,\n",
    "        lw = 2,\n",
    "        guidefontsize = 14)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "\"/Users/uqjnazar/Dropbox/MathEngDeepLearningBook/LaTeXBook/figures/chapter_7_figures/pos_embedding_diff_plot.pdf\""
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "savefig(\"/Users/uqjnazar/Dropbox/MathEngDeepLearningBook/LaTeXBook/figures/chapter_7_figures/pos_embedding_diff_plot.pdf\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
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